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5 Arbitrage and Interest Rates

Recall that most foreign currency operations involve bank deposits. A bank deposit is an

asset that generates interest for the depositor. The decision of where to maintain deposits

is largely a matter of convenience for most. However, for investors, this decision is

known as uncovered interest parity (UIP).

To hedge against exchange rate risk, investors can use derivatives such as forwards.

In this way, the arbitrager eliminates exchange rate risk, that is, he or she is “covered.”

Riskless Arbitrage: Covered Interest Parity

This presentation mirrors the one in the text, but makes use of different exchange rates.

Riskless arbitrage refers to arbitrage that does not involve exchange rate risk. To

Suppose that an American investor Katya is considering whether to put her $800

savings into a U.S. bank account or in a British bank account for the next year. She must

evaluate the expected rate of return from these two investment strategies. (The numbers

used in this example approximate the actual values of the variables as of October 12,

The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This

is the gross dollar return Katya receives from her investment at the end of one year. For

This gain or loss is determined by the forward exchange rate, F$/£ (1.6090), and the

current spot rate, E$/£ (1.6114). Converting one U.S. dollar into British pounds would cost

the forward rate would yield F$/£ dollars. Therefore, the return on British deposits, in U.S.

dollars, is

Utilizing the figures given above, we can use any three variables to calculate the

implied value of the remaining one. For example, the implied value of F$/£ is 1.6076. The

condition yields

APPLICATION

Evidence on Covered Interest Parity

To test whether covered interest parity holds, we can determine whether foreign

exchange traders could, in fact, earn a profit through establishing forward and spot

The data illustrate that arbitrage led to zero profits in the absence of capital controls.

When capital controls are removed, arbitrage profits decrease.

As financial systems become more liberalized, arbitrage opportunities disappear

quickly. When governments imposed capital controls in the foreign exchange market,

Risky Arbitrage: Uncovered Interest Parity

Risky arbitrage does not “cover” investors with a forward contract. Instead, investors

must make their decisions based on what they think the exchange rate will be in the

future. The expected future exchange rate replaces the forward exchange rate in the CIP

example shown previously, and repeated below.

The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This

is the gross dollar return Katya receives from her investment at the end of one year. For

We call this the expected exchange rate, Ee$/£. Given the current spot rate, E$/£ (1.6114)

and the interest rates on the two accounts, we can calculate the market’s forecast of the

But, unlike covered interest parity, the forward exchange rate is not known. The

unknown variable in the uncovered interest parity equation is the expected exchange rate

APPLICATION

Evidence on Uncovered Interest Parity

If the UIP and CIP hold, this implies the forward exchange rate is equal to the expected

future exchange rate. If we divide the CIP condition by the UIP condition, we get

Canceling terms yields

The expression on the left-hand side is the forward premium. To estimate the right-

Uncovered Interest Parity: A Useful Approximation

It will be convenient to use the following approximation:

UIP provides a theory of how expectations are linked to the current spot exchange

rate and to interest rates across countries. Rewriting the UIP condition yields

know that investors expect that the U.S. dollar will depreciate:

6 Conclusions

This chapter provides an overview of exchange rates, the forex market, and the

conditions defining equilibrium in the market, and discusses the ways in which private

actors and the government participate in the forex market. Although there are mainly two

S I D E B A R

Assets and Their Attributes

Investors have many options in holding their wealth. There are many available assets:

cash, stocks, bonds, bank deposits, real estate, and so on. Investors make choices about

how to hold their wealth based on three criteria:

• Rate of return: the net increase in wealth generated from holding the asset.

and services (e.g., the ease with which it can be liquidated or sold). Investors

prefer more liquid assets.

These observations lead to two conclusions. First, investors are willing to trade off more

Teaching Tips

Teaching Tip 1: Uncovered interest parity says the difference between the U.S. interest

rate and the foreign interest rate should equal the expected rate of depreciation of the U.S.

dollar. The Excel workbook for this chapter includes a worksheet that shows comparable

2009 interest rates for a number of countries as well as for the United States. The United

States – foreign difference is also included. Show this table to your students and ask them

to discuss the results. For example, Iceland’s currency is expected to appreciate by

Teaching Tip 2: In this chapter, we assumed frictionless trading in the forex market.

This assumption is relaxed in the last chapter of the textbook. For now, explore the bid-

ask spread with your students. The bid price is the price at which a dealer is willing to

sell a security or currency. The ask price is the willingness-to-buy price. Dealers make a

living on the bid-ask spread. In foreign currency markets, this spread is quoted in pips.

For most currencies, a pip is equal to 0.0001 on the exchange rate. For the yen, however,

one pip is 0.01 of the exchange rate. Exchange rates are conventionally quoted as foreign

currency per U.S. dollar. For example, in the euro–U. S. dollar market, suppose the bid

price is 1.4745 and the ask price is 1.4746. The spread is 1 pip. OANDA’s website offers

a complete list of bid-ask spreads for its trades

IN-CLASS PROBLEMS

1. Use Table 13-1 in the textbook to answer the following questions:

Exchange Rates on June 30, 2010

Exchange Rates on June 30, 2009

(one year previous)

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